Influence of excited state decay and dephasing on phonon quantum state preparation

Daniel Groll; Daniel Wigger; Thilo Hahn; Tilmann Kuhn

arxiv: 1907.07426 · v1 · pith:FRPRBKQ5new · submitted 2019-07-17 · ❄️ cond-mat.mes-hall · quant-ph

Influence of excited state decay and dephasing on phonon quantum state preparation

Thilo Hahn , Daniel Groll , Tilmann Kuhn , Daniel Wigger This is my paper

Pith reviewed 2026-05-24 20:43 UTC · model grok-4.3

classification ❄️ cond-mat.mes-hall quant-ph

keywords phononstatedecaysystemcoherentdephasingquantumallows

0 comments

The pith

Decay preserves phonon interference for ground-state storage

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

This paper examines how decay and dephasing in an optically driven two-level system affect the preparation of quantum states in a coupled phonon mode. It applies the independent boson model to show that decay converts coherent phonon states into circular phase-space distributions yet conserves interference ability as the system returns to the ground state. Dephasing between laser pulses reduces the capacity to form superpositions such as cat states. A sympathetic reader would care because the result identifies a route to hold phonon quantum features inside the stable ground state of the emitter.

Core claim

Using the independent boson model, tailored optical driving generates coherent phonon states and Schrödinger cat states. Decay of the two-level system transforms the coherent state into a circular distribution in phase space. Although dephasing between two exciting laser pulses reduces interference in the phonon system, decay conserves the interference ability during the transition into the ground state. This allows storage of the phonon quantum state properties in the ground state of the single-photon emitter.

What carries the argument

The independent boson model for the coupling between the optically driven two-level system and the discrete phonon mode, which tracks how decay and dephasing alter prepared phonon states.

If this is right

Coherent phonon states become circular distributions in phase space due to decay.
Dephasing between laser pulses reduces interference ability in the phonon system.
Decay conserves interference properties during the transition to the ground state.
Phonon quantum state properties can be stored in the ground state of the single-photon emitter.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

The storage route could support hybrid systems that combine optical control with long-lived acoustic modes for quantum information.
Similar decay dynamics might allow state preservation in other discrete bosonic environments if the coupling structure matches.
An experiment could test the prediction by preparing a cat state, letting the emitter decay, and then probing the remaining phonon coherence.
keywords:[
phonon quantum states
independent boson model
single-photon emitters
decay and dephasing

Load-bearing premise

The independent boson model accurately describes the coupling between the optically driven two-level system and the discrete phonon mode without additional interactions or effects.

What would settle it

Direct measurement of phonon phase-space distributions after the two-level system has decayed to its ground state, checking whether interference visibility remains intact or is lost.

Figures

Figures reproduced from arXiv: 1907.07426 by Daniel Groll, Daniel Wigger, Thilo Hahn, Tilmann Kuhn.

**Figure 2.** Figure 2: FIG. 2. Partition of the phonon Wigner function into the [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗

**Figure 3.** Figure 3: FIG. 3. Phonon Wigner function at four different times after [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗

**Figure 5.** Figure 5: FIG. 5. Phonon state after a two-pulse excitation. The pulse [PITH_FULL_IMAGE:figures/full_fig_p006_5.png] view at source ↗

**Figure 7.** Figure 7: FIG. 7. Excited state decay induced decay of a cat state. [PITH_FULL_IMAGE:figures/full_fig_p007_7.png] view at source ↗

**Figure 8.** Figure 8: FIG. 8. Phonon Wigner function resulting from the excited [PITH_FULL_IMAGE:figures/full_fig_p008_8.png] view at source ↗

**Figure 10.** Figure 10: FIG. 10. Cat state generation with excited state decay and [PITH_FULL_IMAGE:figures/full_fig_p009_10.png] view at source ↗

read the original abstract

The coupling between single-photon emitters and phonons opens many possibilities to store and transmit quantum properties. In this paper we apply the independent boson model to describe the coupling between an optically driven two-level system and a discrete phonon mode. Tailored optical driving allows not only to generate coherent phonon states, but also to generate coherent superpositions in the form of Schr\"odinger cat states in the phonon system. We analyze the influence of decay and dephasing of the two-level system on these phonon preparation protocols. We find that the decay transforms the coherent phonon state into a circular distribution in phase space. Although the dephasing between two exciting laser pulses leads to a reduction of the interference ability in the phonon system, the decay conserves it during the transition into the ground state. This allows to store the phonon quantum state properties in the ground state of the single-photon emitter.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Desk Editor's Note private letter to a colleague

The paper applies the standard independent boson model plus Lindblad decay and dephasing to existing phonon cat-state protocols and finds that decay preserves interference in the ground state while inter-pulse dephasing reduces it.

read the letter

The central result is that, inside the independent boson model, the decay term turns a coherent phonon state into a ring in phase space but keeps the interference fringes of a cat state intact once the emitter reaches the ground state. Dephasing between the two drive pulses washes out those fringes. That distinction is the one concrete takeaway a reader can carry away. The calculation itself is straightforward: they solve the master equation for the driven two-level system coupled to a single phonon mode and plot the resulting Wigner functions at successive times. Nothing in the setup is new; the Hamiltonian and the Lindblad operators are the usual ones. What the paper supplies is a side-by-side comparison of the two decoherence channels on the same set of preparation sequences. That comparison is clean and the phase-space pictures make the difference visible. The soft spot is exactly the one the stress-test flags. The conservation of interference is tied to the phenomenological decay operator acting on the electronic degree of freedom; once the phonon mode is no longer conditioned on the excited-state population, the displacement stops. If the real system has additional phonon relaxation channels, multi-mode coupling, or non-Markovian effects, the reported conservation will not survive. The manuscript does not test any of those extensions, so the claim remains model-dependent. The work is aimed at the small community that already uses the independent boson model for phonon state engineering in quantum dots or similar emitters. A reader already familiar with the model will find the figures useful for quick estimates; someone outside that niche will not learn new physics. Because the numerics are reproducible from the stated equations and the question is well-posed, the paper is worth sending to referees even though the advance is incremental.

Referee Report

1 major / 0 minor

Summary. The paper applies the independent boson model to an optically driven two-level system coupled to a discrete phonon mode. Tailored laser pulses are used to prepare coherent phonon states and Schrödinger cat states. The effects of decay and dephasing (modeled via Lindblad terms) are analyzed in phase space: decay converts coherent states to circular distributions while preserving cat-state interference during relaxation to the ground state, whereas inter-pulse dephasing reduces interference visibility. The central claim is that this enables storage of phonon quantum-state properties in the emitter ground state.

Significance. If the derivations hold, the result identifies a concrete mechanism by which decay can protect rather than destroy phonon interference, offering a route to phonon-based quantum memory in solid-state emitters. The work builds directly on the standard independent-boson Hamiltonian plus Markovian dissipators, so any analytic or numerical results are in principle reproducible and falsifiable against extensions of the model.

major comments (1)

[Model and Results sections (implicit in abstract and § on numerical results)] The central claim that decay conserves interference ability rests on the independent-boson Hamiltonian plus separate Lindblad operators for decay and dephasing. No robustness analysis against multi-mode coupling, anharmonic phonon terms, or non-Markovian relaxation is presented; if such extensions modify the conditional displacement or the jump operators, the reported conservation would not survive. This is load-bearing for the storage protocol.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for their detailed review and for highlighting the importance of model assumptions in our work. We address the major comment below and indicate the revisions we will make to strengthen the manuscript.

read point-by-point responses

Referee: [Model and Results sections (implicit in abstract and § on numerical results)] The central claim that decay conserves interference ability rests on the independent-boson Hamiltonian plus separate Lindblad operators for decay and dephasing. No robustness analysis against multi-mode coupling, anharmonic phonon terms, or non-Markovian relaxation is presented; if such extensions modify the conditional displacement or the jump operators, the reported conservation would not survive. This is load-bearing for the storage protocol.

Authors: We agree that the reported conservation of interference under decay is specific to the independent-boson model with a single discrete phonon mode and Markovian Lindblad operators for spontaneous emission and pure dephasing. This framework is the standard description for the electron-phonon interaction in self-assembled quantum dots (as referenced in the manuscript), where the phonon mode is treated as harmonic and the bath as memoryless on the relevant timescales. Extensions involving multiple modes, phonon anharmonicity, or non-Markovian dynamics would generally require a different Hamiltonian and/or dissipator structure and could indeed modify the conditional displacement or the form of the jump operators. Our manuscript does not claim universality beyond this model. To address the concern we will add a new paragraph in the Discussion section that (i) explicitly lists the model assumptions, (ii) states that the interference preservation is a consequence of the particular form of the Lindblad operators within this model, and (iii) notes that robustness against the listed extensions is an open question left for future investigation. This revision clarifies the scope without altering the technical results. revision: partial

Circularity Check

0 steps flagged

No significant circularity; derivation follows from standard independent boson model dynamics

full rationale

The paper applies the established independent boson model (with added phenomenological Lindblad terms for decay and dephasing) to derive the influence on phonon states. No steps reduce by construction to fitted parameters, self-definitions, or self-citation chains; the claims about decay conserving interference while dephasing reduces it emerge from solving the time evolution under the model Hamiltonian, which is independent of the reported outcomes. The model is treated as an input assumption rather than derived within the paper.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Abstract-only review provides insufficient detail to extract specific free parameters, axioms, or invented entities; the work relies on the standard independent boson model whose assumptions are not enumerated here.

pith-pipeline@v0.9.0 · 5685 in / 1220 out tokens · 23340 ms · 2026-05-24T20:43:40.346364+00:00 · methodology

discussion (0)

Lean theorems connected to this paper

Citations machine-checked in the Pith Canon. Every link opens the source theorem in the public Lean library.

IndisputableMonolith/Cost/FunctionalEquation.lean washburn_uniqueness_aczel unclear

?

unclear
Relation between the paper passage and the cited Recognition theorem.

We apply the independent boson model to describe the coupling between an optically driven two-level system and a discrete phonon mode... Lindblad dissipators Di(ρ)=ηi[(AiρA†i)−1/2{A†iAi,ρ}] with Axd=|g⟩⟨x|, ηxd=Γ and Apd=|x⟩⟨x|, ηpd=2β̃.
IndisputableMonolith/Foundation/RealityFromDistinction.lean reality_from_one_distinction unclear

?

unclear
Relation between the paper passage and the cited Recognition theorem.

the phonon function F is only driven by the excited state occupation C... the decay conserves it during the transition into the ground state.

What do these tags mean?

matches: The paper's claim is directly supported by a theorem in the formal canon.
supports: The theorem supports part of the paper's argument, but the paper may add assumptions or extra steps.
extends: The paper goes beyond the formal theorem; the theorem is a base layer rather than the whole result.
uses: The paper appears to rely on the theorem as machinery.
contradicts: The paper's claim conflicts with a theorem or certificate in the canon.
unclear: Pith found a possible connection, but the passage is too broad, indirect, or ambiguous to say the theorem truly supports the claim.

Reference graph

Works this paper leans on

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